Despite the several available strategies to build complex supramolecular constructs, only a handful of different molecular knots have been synthesised so far. Here, in response to the quest for further designable topologies, we use Monte Carlo sampling and molecular dynamics simulations, informed by general principles of supramolecular assembly, as a discovery tool for thermodynamically and kinetically accessible knot types made of helical templates. By combining this approach with the exhaustive enumeration of molecular braiding patterns applicable to more general template geometries, we find that only few selected shapes have the closed, symmetric and quasi-planar character typical of synthetic knots. The corresponding collection of admissible topologies is extremely restricted. It covers all known molecular knots but it especially includes a limited set of novel complex ones that have not yet been obtained experimentally, such as 10124 and 15n41185, making them privileged targets for future self-assembling experiments.

Phase separation is as familiar as watching vinegar separating from oil in vinegrette.The observation that phase separation of proteins and nucleic acids is widespread in living cells has opened an entire field of research into the biological significance and the biophysical mechanisms of phase separation and protein condensation in biology. Recent evidence indicate that certain proteins and nucleic acids condensates are not simple liquids and instead display both viscous and elastic behaviours, which in turn may have biological significance. The aim of this perspective is to review the state-of-the-art of this quickly emerging field focusing on the material and rheological properties of protein condensates. Finally, we discuss the different techniques that can be employed to quantify the viscoelasticity of condensates and highlight potential future directions and opportunities for interdisciplinary cross-talk between chemists, physicists and biologists.

In this theoretical study we discuss a novel method for sorting ring polymers according to their topological, knotted state. The proposed approach harnesses the rich dynamical behaviour of polymers confined inside spatially-modulated nanochannels. The longitudinal mobility of the rings is shown to have two key properties that are ideally suited for knot sorting. First, at fixed topology, the mobility has an intriguing oscillatory dependence on chain length. Second, the mobility ranking of different knot types is inverted upon increasing the chain length. We show that this complex interplay of channel geometry, chain length and topology can be rationalised within a simple theoretical framework based on Fick-Jacobs's diffusive theory. The results and the interpretative scheme ought to be useful for designing microfluidic devices with optimal topological sorting capabilities.

No abstract